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Leibniz-Handschriften zur Mathematik LH 35, 3 B 20, fol. 10r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.70.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.

The machine reads it as

  1. prop. VI)
  2. 1
  3. Invenire ticequadratos progressionis
  4. L
  5. e eernee in uite linostenditur
  6. ese
  7. simul eorum differentiant non posse essequadratum
  8. a
  9. G
  10. Arithmet
  11. erit 2y aequ. X
  12. sint illi X. V.
  13. sete eaeq fiat, xaequ y 43 Et Q aequ ∞+3.
  14. v
  15. fiet: y+is aequ y 2y7 +Z + y + 27Z+3
  16. urqi
  17. seu y aequ. 5- . fiat 2- Z aequ n erit
  18. 2, 7-3
  19. 3 aequ. M + Z.
  20. + 2ZM+ 2V 59
  21. Ergo y aequ. C
  22. (10). 2β
  23. 3
  24. a a d. seu y aequ (2+Z +3
  25. e
  26. 2 n
  27. e
  28. Loco, ( scribe l4. et loco _ 3 scrite Ai, seu 2s β
  29. fiet: y aequ (+ 2AB + 2 A B
  30. v
  31. X p per aequ. 2. 6. fit X aego β + 2AB+cAB, 2B- A P
  32. 1.)
  33. B seu X aequ2AB - B it Et per aequ. 3. 11 fres
  34. 13
  35. e Z aequ B+ 2dB + 2Nβ + 2Aβ.
  36. Ergo Z aequ β + 4 AB + 2A B
  37. aequ (2β 8A β7 81
  38. ss
  39. d
  40. a
  41. se
  42. V
  43. aequ B( 8 A B A a AB
  44. al
  45. 2
  46. Hinc ergo
  47. sa
  48. ays + 16 3
  49. a
  50. aequ. sa e A β A AB
  51. 22
  52. a
  53. et
  54. +8
  55. 16A 416 Vβ + (45
  56. ss
  57. d
  58. Unde patet. X + Z esse aequ. 2y qut desiderabatur
  59. si ponatitur β et A. esse T. fet. Laq.
  60. fiet X aequ. 1. et y aequ. 5 et Z aequ. 7.
  61. nam 1. 25. 49. sunt tria quadrata
  62. progressionis arithmeticae omnium possibilium
  63. extrima
  64. simplicissima.
  65. Defferentia inter Z et X, est: eAB + d4 A β + 165
  66. cinus dimidium +AB Y 124 B. + 53B? est differentia 4.
  67. u hujus arithimetic
  68. dunce dividengoi
  69. ests quadratus, ut alionde puctt, ergu +
  70. foret quadratus. Sed hoc impossibile esse patet, quia hujus
  71. Naculo gisinis.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 20, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068269:0019?run=74